Problem: What do the following two equations represent? $3x+5y = -5$ $-25x+15y = 2$
Explanation: Putting the first equation in $y = mx + b$ form gives: $3x+5y = -5$ $5y = -3x-5$ $y = -\dfrac{3}{5}x - 1$ Putting the second equation in $y = mx + b$ form gives: $-25x+15y = 2$ $15y = 25x+2$ $y = \dfrac{5}{3}x + \dfrac{2}{15}$ The slopes are negative inverses of each other, so the lines are perpendicular.